Page "Fractional ideal" Paragraph 1

Let R be an integral domain, and let K be its field of fractions.

A fractional ideal of R is an R-submodule I of K such that there exists a non-zero r ∈ R such that rI ⊆ R. The element r can be thought of as clearing out the denominators in I.

The principal fractional ideals are those R-submodules of K generated by a single nonzero element of K. A fractional ideal I is contained in R if, and only if, it is an (' integral ') ideal of R.